The problem of supplying a suitable quantity of fossil fuels has focused increased attention on the higher molecular weight fossil fuels, both petroleum and synthetic oils, such as those derived from coal, shale and tar sands. Such oils in many cases contain metal compounds and/or sulfur compounds or nitrogen compounds which complicate the problem of catalytic conversion of such oil, such as cracking, and hydro treating processes, for example, hydroforming, hydrocracking, hydro-desulfurization. Catalysts and substrates employed by the prior art in producing such catalysts are porous with heterogeneous assembly of pores of various shapes and sizes.
It is quite generally recognized that it is desirable that the catalysts for such process and the substrates employed producing the catalysts have available pore volume and available surfaces which are in pores of the larger sizes and that there be only minor portion of the available pore volume and pore surfaces in the pores of the smaller sizes. See for example U.S. Pat. Nos. 2,890,162, and 3,944,482.
The identification of volume and surface areas of pores of various configurations in any system of pores in a porous solid is still empirically determined. A common method is to employ nitrogen to develop an adsorption isotherm and also in some cases a desorption isotherm. The value of the total pore volumes, the total surface area of the pores of a porous solid are determined from the isotherms (see Brunauer "Adsorprtion Of Gases And Vapors", vol. 1, Princeton Univ. Press, 1943, Brunauer et al., J.A.C.S., vol. 60, pg. 309 etc. (1938).
The distribution of the values of the pore volume and surface area in various ranges of the equivalent pore diameters in a heterogeneous pore structure may be determined from the nitrogen isotherms.
A widely used apparatus and that used in the following examples for determination of the above parameters for nitrogen isotherms employs a computerized apparatus. (Digisorb 2500 manufactured by the Micromeritic Instrument Corp. of 5680 Goshen Springs Road, Norcross, Ga. 30071.)
The procedure employing this instrument determines the parameters for a nitrogen adsorption and a desorption isotherm and determines the so-called B.E.T. surface area by application of equation as given on page 312 of the above J.A.C.S. article (known as the B.E.T. equation). The slope and intercept of the linear relation according to that equation is determined. The equation evaluates the volume of the gas as a mono molecular layer of nitrogen adsorbed on the surfaces of the pores. From the known diameter of the nitrogen molecule and the volume of the monolayer, the magnitude of the surface of the pores carried by the mono layer is evaluated. To evaluate the slope and intercept of the above linear relation, the separate values of the relative pressure (P/Po) of the selected portion of the isotherm are chosen. P is the local pressure selected and Po is the saturation pressure. The linear relation is determined as the least square fit to the above B.E.T. linear equation.
The B.E.T. surface area (S) in meters square per gram is given by the following equation which includes the value of the area covered by the nitrogen molecule 16.2A.sup.2. According to the equation: ##EQU1## where S is the surface area in square meters per gram (M.sup.2 /gm); "a" is the above intercept of the linear relation and "b" is the slope of said linear relation. This value is referred to as the BET surface, and is so referred to in this application.
The pore volume is determined from the volume of nitrogen gas adsorbed at saturation evaluated at standard conditions converted to liquid nitrogen by multiplying the volume of gaseous nitrogen adsorbed at standard conditions by the factor 1.558.times.10.sup.-3 to yield the equivalent volume of adsorbed nitrogen in cc/gm herein referred to as "Specific Pore Volume".
In determining the distribution of the pore volume and pore surfaces in the pores of various diameters in the sample, the Kelvin radius, which assumes a cylindrical pore is determined corresponding to the various levels of relative pressures in the isotherms. Adjustment is made to reflect the thickness of the adsorbed nitrogen in the pores as a function of the various relative pressures (P/P.sub.o) of the isotherms.
The thickness of the adsorbed nitrogen (t) is given by: ##EQU2## where ln P/P.sub.o is the natural log of the relative pressure P/P.sub.o of the selected portion of the desorption isotherm.
To evaluate the surface area (M.sup.2 /gm) and pore volume (cc/gm) in the pores of different pore radii corresponding to the various values of (P/P.sub.o) along the isotherms (in the present case, the desorption isotherm), the following relation is followed in the above Digisorb apparatus. The values of pore volume and pore surface stated in the following portion of this specification are those derived from this apparatus.
The radius (r) is the so-called Kelvin radius derived from the Kelvin equation (See Brunauer "Adsorption of Gases And Vapors" and Lippius et al, "Journal of Catalysis", vol. 3, page 32 at p. 35 (1964)). The radius of the pore is taken as: ##EQU3## where r is the radius of the pore; t is the thickness and r is the portion of the radius which is not occupied by the layer thickness (t). Each increment of condensate desorbed as the relative pressure is decreased in the developed desorption isotherm, is comprised of gas evaporated from pores that were previously filled with liquid and from the surface of unfilled pores. EQU Dv.sub.p =Dv-Dv.sub.s
Dv is obtained directly from the desorption isotherm. EQU Dv.sub.s =Dt.SIGMA.DS.sub.p
where Dt is the change in thickness t, and .SIGMA.DS.sub.p is all pore surface area other than those of the filled pores. For each desorption increment the surface area attributable to any group of pores of radius r.sub.1 and r.sub.2 is given by the following: ##EQU4## where r.sub.c is the average of the group r.sub.1 -r.sub.2, i.e., 0.5(r.sub.1 +r.sub.2) pore radii desorbed and DV.sub.p is the corresponding pore volume of the group and is given by ##EQU5## Since the desorption isotherm is measured in terms of gas volume at standard conditions and the surface area and pore volume as above requires the conversion to equivalent liquid parameters the above conversion of the isotherm data to surface area and pore volume employing the above constants are applied here also. (See equation 1 and conversion factors). The equivalent pore volume and pore surface area for each pore radius interval is obtained by applying the above computation scheme.
The volume v.sub.1 of liquid desorbed from one pore radius r.sub.o to the next smaller pore radius r.sub.1, and is given by the following relation ##EQU6## Where r.sub.1 is the average next smaller interval 0.5r.sub.0 -r.sub.1) and (t) is the thickness at r.sub.1 (Equation 2). EQU q=v.sub.o -v.sub.1
q is equal to the volume of gas (as liquid) desorbed between radius r.sub.o and r.sub.1, v.sub.o is the volume of gas (as liquid) adsorbed at r.sub.o and v.sub.1 is the volume of gas adsorbed (as liquid) at r.sub.1. t has the meaning of Equation 2.
The pore volume and pore surface corresponding to each increment of relative pressure of the desorption isotherm and the corresponding volume and corresponding average of the corresponding pore radii may then be determined by applying the above consideration to each step of the desorption isotherm. The above computation scheme is applicable down to 10 Angstrom radius.
The relation of the surface area in the pores of radius r corresponding to the increment of desorbed gas (as liquid) is given by the following relation ##EQU7##
From the above, the value of the pore volume is evaluated as cubic cm per gram (cc/gm) and the value of the pore surface (evaluated as meters square per gram (M.sup.2 /gm)) for each selected interval of pore radii (or diameter) corresponding to the equivalent interval of the relative pressure (P/P.sub.o) of the isotherm, in the present case, from the desorption isotherm. In the case of the examples reported, the ranges of the intervals of (P/P.sub.o) of the desorption isotherm were selected to be equivalent to the following intervals of radii r.sub.1 and r.sub.2. For diameters between 20 to 100 Angstroms, the interval is 5 Angstroms; between 100 and 160 Angstroms, the interval is 10 Angstroms: between 160 and 300 Angstroms, the interval is 20 Angstroms; between 300 and 500 Angstroms, the interval is 50 Angstroms; and between 500 and 600 Angstroms, the interval is 100 Angstroms.
The values of pore volume and pore surface for any greater interval are obtained by summing the pore surfaces and pore volumes in the pores of each of the smaller intervals contained in the greater interval to wit 20 to 50; 50 to 200 and 200 to 600 Angstroms diameters. The intervals of radii as stated above signify that the radii is more the lowest value for example 20, and less than the highest value, for example 50 Angstroms diameter.
The surface areas and pore volume for the several ranges of pore diameter and the total pore volume and surface are obtained and determined from the desorption isotherms and herein referred to as the "desorption area", or the "desorption pore volume".
Where in this specification we refer to pore volume either generally or by number, the reference is intended to be evaluated per gram of the gel on a dry basis such as obtained by drying at 100.degree. C. for a prolonged period of time or or as specified after calcining the gel as for example at 1000.degree. F. for several hours.